# Thread: Curve Sketching

1. ## Curve Sketching

Show that for any cubic function of the form y = ax3 + bx2 + cx + d, there is a single point of inflection where the slope of the curve at that point is C – b2 / 3a.

2. I would suggest making $\frac{dy}{dx} =$
Originally Posted by steezin
C – b2 / 3a.

3. Originally Posted by steezin
Show that for any cubic function of the form y = ax3 + bx2 + cx + d, there is a single point of inflection where the slope of the curve at that point is C – b2 / 3a.
It follows from the definition that the x-coord of the point of inflection occurs where dy/dx has a turning point.

4. Originally Posted by steezin
Show that for any cubic function of the form y = ax3 + bx2 + cx + d, there is a single point of inflection where the slope of the curve at that point is C – b2 / 3a.
Sounds straightforward to me. An inflection point occurs where the second derivative is 0. Set the second derivative equal to 0 and solve for x. Then calculate the first derivative for that x.